Here we will explain what 135 mod 12 means and show how to calculate it. 135 mod 12 is short for 135 modulo 12 and it can also be called 135 modulus 12.
Modulo is the operation of finding the Remainder when you divide two numbers. Therefore, when you ask "What is 135 mod 12?" you are asking "What is the Remainder when you divide 135 by 12?".
We will show you two methods of finding 135 mod 12 (135 modulo 12). To differentiate our methods, we will call them the "Modulo Method" and the "Modulus Method".
Before we continue, we remind you of what the different parts of a division problem are called so you can follow along: Dividend / Divisor = Quotient and in this case 135 is the Dividend, 12 is the Divisor, and the answer is called the Quotient.
Furthermore, the Quotient x.y has two parts: x to the left of the decimal point is the Whole part, and y to the right of the decimal point is the Fractional part.
Modulo Method
To find 135 mod 12 using the Modulo Method, we first divide the Dividend (135) by the Divisor (12).
Second, we multiply the Whole part of the Quotient in the previous step by the Divisor (12).
Then finally, we subtract the answer in the second step from the Dividend (135) to get the answer. Here is the math to illustrate how to get 135 mod 12 using our Modulo Method:
135 ÷ 12 = 11.25
11 × 12 = 132
135 - 132 = 3
Thus, the answer to "What is 135 mod 12?" is 3.
Modulus Method
To find 135 mod 12 using the Modulus Method, we first find the highest multiple of the Divisor (12) that is equal to or less than the Dividend (135).
Then, we subtract the highest Divisor multiple from the Dividend to get the answer to 135 modulus 12 (135 mod 12):
Multiples of 12 are 0, 12, 24, 36, etc. and the highest multiple of 12 equal to or less than 135 is 132. Therefore, to get the answer:
135 - 132 = 3
Thus, once again, the answer to "What is 135 mod 12?" is 3.
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